This type of fluid product dispenser distributes a mix of gas, usually air, and liquid or powder fluid product. Dispensing is therefore of the two-phase type in the form of an atomised jet in which fine droplets or grains are transported in an air stream. For example, document FR 2 748 407 describes a two-phase atomiser. The atomiser described in this document comprises a fluid product pump mounted on a fluid product reservoir. The pump comprises a pusher installed on the pump actuating stem. An air pump is formed inside the pusher around the actuating stem. This air pump is defined by a chamber inside which a piston slides in a leak tight manner. Furthermore, the pusher comprises a dispensing orifice that is supplied with a fluid product from the pump and air from the air chamber. Thus, there is an atomised two-phase dispensing at the exit of the dispensing orifice. Therefore, the atomiser or sprayer described in this document uses a pressurisable air reservoir and a fluid product reservoir with which a pump is associated to draw off the fluid product in the reservoir and to transport it to the dispensing orifice. The function of the pusher is to activate the pump and simultaneously pressurise the air contained in the air chamber. The effect of actuating the pusher is not to increase the pressure inside the fluid product reservoir, since the pump is inserted between the pusher and the fluid product reservoir.